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Air Elimination in Milk Pump Systems

30 November 2011
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Executive summary

This report summarises the work done by the Mathematics Applications Consortium for Science and Industry (MACSI) in Ireland on simulating a new design of milk metering equipment for Piper Systems Ltd.

Challenge overview

During collection, milk is pumped from a farm tank by a centrifugal pump into an air elimination vessel. After passing through the vessel, the volumetric flow rate is measured and the total amount of milk is calculated. Piper Systems manufacture the on board metering equipment carried by milk trucks. The managing director approached MACSI to ask for their help with

(i) modelling the existing setup (shown in the figure) to understand and quantify any sources of error that might be introduced;

(ii) modelling a new proposed new design of the milk metering equipment to see if it would improve the accuracy of measurements and to see if any optimisation of the design could produce further reductions in errors.

Implementation of the initiative

After a half day MACSI workshop with postgrads, postdocs and research fellows from MACSI as well as the MD of Piper Systems Ltd. a team with the most relevant experience was chosen to work on the problem over a 1 year period. A collaborative research agreement between the University of Limerick and Piper Systems Ltd. was drawn up.

The problem

The first stage of the problem was to simulate the entire system to demonstrate that the proposed design would successfully pump milk. The system was modelled by a system of non linear ordinary differential equations which were derived and solved numerically. The next stage of the problem was to model the motion of the milk and the formation of bubbles within an air elimination vessel. Partial differential equations were derived for both cases, simplified and solved.

Results and achievements

Results were obtained by solving the equations mentioned above and recommendations were made regarding different parameters and physical dimensions of the system. These should help the company modify the design of the milk metering equipment for optimum performance which could potentially increase sales by up to €0.5 million. 

Figure 1: Generic farmer's tank and pump schematic.


Archie Hamilton, MD
Bray Co Wicklow
Ireland Tel: +353 (0)1 2829844

Attached Documents

PDF icon Irish Mathematics and Industry (Irish_Mathematics_and_Industry.pdf | 1.42 MB)